const SNoCutP : set set prop const SNo : set prop const SNoCut : set set set axiom SNoCutP_SNo_SNoCut: !x:set.!y:set.SNoCutP x y -> SNo (SNoCut x y) const In : set set prop term iIn = In infix iIn 2000 2000 const SNoLt : set set prop term < = SNoLt infix < 2020 2020 lemma !x:set.!y:set.!z:set.!w:set.SNoCutP x y -> SNoCutP z w -> (!u:set.u iIn x -> u < SNoCut z w) -> (!u:set.u iIn y -> SNoCut z w < u) -> (!u:set.u iIn z -> u < SNoCut x y) -> (!u:set.u iIn w -> SNoCut x y < u) -> SNo (SNoCut x y) -> SNo (SNoCut z w) -> SNoCut x y = SNoCut z w var x:set var y:set var z:set var w:set hyp SNoCutP x y hyp SNoCutP z w hyp !u:set.u iIn x -> u < SNoCut z w hyp !u:set.u iIn y -> SNoCut z w < u hyp !u:set.u iIn z -> u < SNoCut x y hyp !u:set.u iIn w -> SNoCut x y < u claim SNo (SNoCut x y) -> SNoCut x y = SNoCut z w